Module 10 Assignment

Daniel Tafmizi

Lis 4273

Dr. Ajani 

March 24, 2024

Module 10 Assignment

9.1. 

library(ISwR)

data <- (cystfibr)

x <- lm(formula = cystfibr$pemax ~ age + weight + bmp + fev1, data=cystfibr)

anova(x)         

Analysis of Variance Table

Response: cystfibr$pemax

           Df  Sum Sq Mean Sq F value    Pr(>F)    

age        1 10098.5 10098.5 18.4385 0.0003538 ***

weight     1   945.2   945.2  1.7258 0.2038195    

bmp        1  2379.7  2379.7  4.3450 0.0501483 .  

fev1       1  2455.6  2455.6  4.4836 0.0469468 *  

Residuals 20 10953.7   547.7   

With the given model, we are testing the statistical significance between pemax to the other groups.

Given the low P-values, we can say that age and fev1 are significantly related to pemax. However, given the high p-values, we can say weight and bmp do not have a significant relation to pemax

Coefficients:

  (Intercept)          age       weight          bmp         fev1  

      179.296       -3.418        2.688       -2.066        1.088 

      

For every unit increase in age, the pemax goes down 3.418 units.      

For every unit increase in weight, the pemax goes up 2.688 units.

For every unit increase in bmp, the pemax goes down 2.066 units.

For every unit increase in fev1, the pemax goes up 1.088 units.

This tells us that an increase in age or body mass has a negative effect on maximum respiratory pressure. Adjusted for the other 3 terms in the model.

That an increase in weight or fev1 has a positive effect on maximum respiratory pressure. Adjusted for the other 3 terms in the model.

9.2 

data2 <- secher

bwtlog <- log(secher$bwt)

bpdlog <- log(secher$bpd)

adlog <- log(secher$ad)

model <- lm(bwtlog~bpdlog + adlog)

summary(model)

Call:

lm(formula = bwtlog ~ bpdlog + adlog)

Residuals:

  Min       1Q   Median       3Q      Max 

-0.35074 -0.06741 -0.00792  0.05750  0.36360 

Coefficients:

  Estimate Std. Error t value Pr(>|t|)    

(Intercept)  -5.8615     0.6617  -8.859 2.36e-14 ***

  bpdlog        1.5519     0.2294   6.764 8.09e-10 ***

  adlog         1.4667     0.1467   9.998  < 2e-16 ***

  ---

  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1068 on 104 degrees of freedom

Multiple R-squared:  0.8583, Adjusted R-squared:  0.8556 

F-statistic: 314.9 on 2 and 104 DF,  p-value: < 2.2e-16

model2 <- lm(bwtlog~adlog)

summary(model2)

Call:

  lm(formula = bwtlog ~ adlog)

Residuals:

  Min       1Q   Median       3Q      Max 

-0.58560 -0.06609  0.00184  0.07479  0.48435 

Coefficients:

  Estimate Std. Error t value Pr(>|t|)    

(Intercept)  -2.4446     0.5103  -4.791 5.49e-06 ***

  adlog         2.2365     0.1105  20.238  < 2e-16 ***

  ---

  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1275 on 105 degrees of freedom

Multiple R-squared:  0.7959, Adjusted R-squared:  0.794 

F-statistic: 409.6 on 1 and 105 DF,  p-value: < 2.2e-16

Both show statistical significance between birthweight ~ (bpd + ad) or (ad).

However, the use of both bpd and ad offers more precise analysis. The coefficients add to 3.0186. This

tells us that for every unit increase in ad and bpd, the btw increases by 3.0186.

When only analyzing ad, we see that for every unit increase in ad, the btw increases by 2.365.